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INVARIANT TWINS
Sylvester's wide range of reading from the credited quotations
and the curious hints thrown out without explicit reference. In
addition to the English and classical literatures he was well
acquainted with the French, German, and Italian in the ori-
ginals. His interest in language and literary form was keen and
penetrating. To him is due most of the graphic terminology of
the theory of invariants. Commenting on his extensive coinage
of new mathematical terms from the mint of Greek and Latin,
Sylvester referred to himself as the 'mathematical Adam'.
On the literary side it is quite possible that had he not been a
very great mathematician he might have been something a
little better than a merely passable poet. Verse, and the 'laws*
of its construction, fascinated him all his life. On his own
account he left much verse (some of which has been published),
a sheaf of it in the form of sonnets. The subject-matter of his
verse is sometimes rather apt to raise a smile, but he frequently
showed that he understood what poetry is. Another interest on
the artistic side was music, in which he was an accomplished
amateur. It is said that he once took singing lessons from
Gounod and that he used to entertain working-men's gather-
ings with his songs. He was prouder of his 'high C* than he was
of his invariants.
One of the many marked differences between Cayley and
Sylvester may be noted here: Cayley was an omnivorous reader
of other mathematicians' work; Sylvester found it intolerably
irksome to attempt to master what others had done. Once, in
later life, he engaged a young man to teach Mm something
about elliptic functions as he wished to apply them to the
theory of numbers (hi particular to the theory of partitions,
which deals with the number of ways a given number can be
made up by adding together numbers of a given kind, say all
odd, or some odd and some even). After about the third lesson
Sylvester had abandoned his attempt to learn and was lecturing
to the young man on his own latest discoveries in algebra. But
Cayley seemed to know everything, even about subjects in
which he seldom worked, and his advice as a referee was sought
by authors and editors from all over Europe. Cayley never for-
got anything he had seen; Sylvester had difficulty in remem-
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